Exterior (topology)

In topology, the exterior of a subset S of a topological space X is the union of all open sets of X which are disjoint from S. It is itself an open set and is disjoint from S. The exterior of S is denoted by

ext S

or

Se.

Equivalent definitions

The exterior is equal to X \ , the complement of the topological closure of S and to the interior of the complement of S in X.

Properties

Many properties follow in a straightforward way from those of the interior operator, such as the following.

Unlike the interior operator, ext is not idempotent, but the following holds:

See also

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